Two polarising sheets are placed parallel with their  polarising axes. The intensity of emergent light is I_m  Now, one of the sheets is rotated through an angle $\theta$. If the intensity of emergent light is reduced to half $\left(\text{ i.e. },\frac{{\mathrm{I}}_{\mathrm{m}}}{2}\right)$ then the angle $\theta$ will be

• A

  $\pm {30}^{\circ }\text{ and }\pm {135}^{\circ }$

• B

  $\pm {45}^{\circ }\text{ and }\pm {120}^{\circ }$

• C

  $\pm {30}^{\circ }\text{ and }\pm {120}^{\circ }$

• D

  $\pm {45}^{\circ }\text{ and }\pm {135}^{\circ }$